Thursday, March 31, 2011

Chemists and physicists tend to talk different languages, including when discussing the same thing. One important parallel is the common concept of the molecular orbitals in a molecule and the energy bands in a crystal. Specifically, the Huckel method to describe electronic properties of conjugated organic molecules is identical to the tight-binding method in solid state physics.

Yet these important parallels seem to rarely be pointed out in textbooks. [One exception is a brief mention in Walter Harrison's Electronic Structure and the Properties of Solids].
Recently when I have taught solid state I have pointed out the connection and sometimes worked through the nice treatment of Huckel theory in chapter 8 of the classic book Coulson's Valence by Roy McWeeny.

Besides showing the molecule-solid connection this can illustrate a few useful things including:

How Bloch's theorem works in a finite system.

How energy bands emerge in the thermodynamic limit (see above).

The correspondence between bonding (anti-bonding) orbitals in a molecule and valence (conduction) bands in a crystal.

The potential importance of electron-electron interactions, which are completely neglected in both Huckel and tight-binding approximations. Valence bond theory takes these interactions into account.

Wednesday, March 30, 2011

Here are a few reasons why you should work hard at picking the title of your papers.

* They are one of your only chances to get people interested in actually reading your paper.

* When people are reviewing your CV many will just look at the title of your papers, as well as the journal they are published in. Interesting, diverse, informative, and understandable titles create a good impression. Boring, repetitive, and highly technical titles create a bad impression. Make sure all your papers don't have essentially the same title!

* They are fun.

What I generally do is to write down as many as five possible titles for the paper and then consider their relative merits and discuss them with co-authors and colleagues. This helps sharpen the title.

In German ansatz means "educated guess".
For quantum many-body physics two dimensions is very different to one.

In the last two days I have heard talks from graduate students of my UQ colleague Guifre Vidal [who is moving to Perimeter Institute] about using tensor network states to describe quantum many-body states. A nice statement of the problem and the approach is in a Physics Viewpoint by Subir Sachdev.

It is first important to appreciate that Tensor Network states are essentially a convenient way to write a variational wave function for the ground state of a quantum many-body system. Like any such wave function they will only be useful/accurate/reliable if this choice is specific enough to capture the essential physics and/or if it is general enough to describe any state. Writing down a good variational wave function is an art worthy of a Nobel Prize (BCS, Laughlin, Anderson,...).

The one-dimensional version of a Tensor Network is a matrix product state (MPS). They work extremely well in one dimension because they can capture all the quantum entanglement. Essentially what the DMRG (Density Matrix Renormalisation Group) does is find MPS states. It seems that MPS can be used to represent the ground state of any physically reasonable Hamiltonian with short range interactions.

But how about in two dimensions? As Sachdev says,

There is an alphabet soup of proposals [5], including MPS, projected entangled-pair states (PEPS), multiscale renormalization ansatz (MERA) [6], tensor renormalization group (TRG) [7], and now the tensor entanglement-filtering renormalization (TEFR) of Gu and Wen. These methods are connected to each other, and differ mainly in the numerical algorithm used to explore the possible states. So far no previously unsolved model H has been moved into the solved column, although recent results from Evenbly and Vidal [8] show fairly conclusive evidence for VBS order on the kagome lattice, and there is promising progress on frustrated square lattice antiferromagnets [9].

However, since Sachdev wrote that in 2009 it turns out that these results for the Kagome model turned out not to get the correct ground state. So it is still not clear that these are appropriate and useful variational wave functions for two dimensions.

Should we be optimistic? We need to keep in mind that two dimensions is a lot richer and more complicated than one dimension. There are many unique things about one dimension which greatly restrict the possible type of quantum many-body states one can have. One can only scatter particles forward and backwards. One cannot have any continuous broken symmetries. Many quantum lattice models are integrable. Conformal field theory provides a means to classify all possible critical theories.... Nevertheless, it is surprising to me that MPS can capture all states.

In contrast, experiment shows that two dimensions produces a plethora of strange ground states in two dimensions, e.g., high-Tc superconductors, strange metals, non-Fermi liquids, topological order, spin liquids, fractional quantum Hall effect with quasi-particles with anyonic statistics. Hence, I will be surprised (and delighted) if one can really capture all these states in terms of just one class of wavefunctions such as PEPS.

Tuesday, March 29, 2011

What is the ground state of the two-dimensional Hubbard model? What "causes" high-Tc superconductivity: is it antiferromagnetic fluctuations, condensation of "pre-formed pairs", or proximity to the quantum critical point of a d-density wave state, or something else?

I read a nice paper today d-Mott phases in One and Two Dimensions by Andreas Lauchli, Carsten Honerkamp, and Maurice Rice, which highlights to me why it is so hard to answer the above questions. But it does gives some clues about the essential physics.

They start with a Hubbard model in the weak coupling limit. Momentum space is divided up into a few "patches" and one performs renormalisation on a reduced Hamiltonian defined on these patches. New effective interactions arise as a result of this renormalisation.

There is a mutual reinforcement of antiferromagnetic (AF) and d-wave pairing tendencies [both superconducting and d-density wave] when the Fermi energy is close to the van Hove singularities at the saddle points (SP) (0,pi) and (pi,0) [i.e. close to half filling]. A key point: the same physics occurs in the half-filled 2-leg Hubbard ladder (2LHL), a model which has an RVB ground state.

The basis of this mutual reinforcement of these different scattering/interaction channels is simple geometry. A significant fraction of particle pairs that experience strong umklapp scattering in the (pi,pi) channel, e.g., two particles close to (pi,0), have small total momentum and thus also couple into the Cooper pair channel .

The figure below shows some of these scattering processes between patches.

For strong enough coupling and small enough doping a charge and spin gap opens up on the patches at (0,pi) and (pi,0). This corresponds to the pseudogap state.

The left hand figure below shows the gaps for spin, two particle, and single particle excitations as a function of the coupling constant and energy cutoff.

The right figure shows the magnitude of the structure factor for different channels.

These enhanced correlations in more than one channel means that

a simple mean-field theory cannot capture the character of the ground state

different ordered states will be close in energy and so numerical methods with a particular bias may pick out the wrong ground state.

A few questions:

Does similar physics apply in the Hubbard model on the anisotropic triangular lattice at half filling? I cannot see why not.

How will the mutual reinforcement be modified by a large magnetic field?

One of the main results of the paper is that as one increases the number of thiophene groups in the middle of the molecule the energy gap to the lowest optically active state decreases, the amount of biradical character of the ground state increases and there is a lower lying "dark" state which has "double exciton" character, analogous to the 2A_g state in polyenes.

Below are the possible valence bond diagrams for hexatriene. There is a one-to-one mapping of these states to the valence bond states of the quinoidal thiophene molecule shown on the bottom left above [denoted 2P-1T in the paper]. In particular, the "quinoidal" and "biradicaloid" states correspond to stuctures R_1 and R_k below, respectively.

The contribution of these different valence bond states to the low lying excited states is shown below.

The relative energies and coupling matrix elements between the different VB states will determine the character of the ground and first excited state.

Saturday, March 26, 2011

Over the years I have made many visits to different institutions, hosted many visitors, and met with many visitors at my home institution. These interactions have varied greatly in their value and success. Some have been incredibly interesting and fruitful. Indeed, many of my best new research ideas have had their beginnings in such discussions. On the other hand, some of the meetings seem to be rather "slow" and a waste of time. So here are a few thoughts on making the most of these meetings, from both sides.

The better prepared you are the greater the chance of a productive meeting. You want to find some common ground and common interest, i.e., something they have done you need to know about or something you have done you would like them to know about.

A minimum preparation is to scan the titles of the publications of the person you are meeting with. This will hopefully help find some common interests. Perhaps pick one paper that you would most like to ask them about.

Bring some "props" to the meeting. A printout of a recent talk you gave or a few powerpoint slides can help focus discussion. But don't rehash the whole talk. Share just a few highlights to gauge interest. If they want to know all the technical details they will ask. Bringing a copy of a recent paper to give away is good. They may even read it on the flight home!

Be a good listener. Be more eager to hear about their work than talk about your own.

For junior people meeting with senior people these meetings can be important career wise. Creating a good impression may lead to an invited talk at a conference, a sympathetic review of your next paper, or even a job offer. Giving a bad impression may lead to ... none of these. Hence, being well prepared is a good investment.

Overall I think everyone's goal should be to learn at least one interesting new piece of science.

Upon photoexcitation the auramine dye molecule (below) is believed to undergo twisting of the phenyl (benzene) rings on the left and right side of the central C=NH2 bridge. With increasing time [1-100 psec] this leads to redshift in the light emission frequency [dynamic Stokes shift] and a reduction in the intensity of emission. As the temperature decreases and the viscosity of the solvent increases the time scale on which these changes occur increases.

Here are a few of the key ideas and things I found interesting about the paper.

They consider four alternative physical models to explain the experiments and rule out three of them. The best model consists has the excited state being a superposition of a two diabatic states: one fluorescent F and one dark D. As the reaction proceeds (the molecule twists) the character of the state changes from F to D.

Dynamics on the excited state potential energy surface is described by a Schmoluchowski equation with a rotational diffusion constant Dr.

Comparing the predictions of the model with experimental data they find that the diffusion constant Dr increases with the temperature and with the inverse of the solvent viscosity. The magnitude of this dependence is consistent with the Einstein-Stokes relation. This shows that the twisting motion of the molecule is overdamped by collisions with the solvent molecules. [Since the solvent is non polar dielectric relaxation is not involved].

A key next step is to provide a quantum chemical justification for the model, both the existence of the dark excited state and the relevant parameters in the effective Hamiltonian for the excited state.

Thursday, March 24, 2011

It is amazing but I never took an introductory Solid State Physics course, either as an undergraduate or as a graduate student! As an undergraduate at ANU, the course was an elective and so I avoided the course because my previous experience with the lecturer was he was incompetent. At Princeton I had to pass a "General exam" which covered solid state, nuclear, particle physics, and general relativity. I taught myself solid state physics by reading a library copy of Ziman's Principles of the Theory of Solids. I don't remember why I made this choice but I suspect it was partly that Solid State Physics by Ashcroft and Mermin seemed too big.

I bought a second hand copy of Ashcroft and Mermin when I was a postdoc, but only started to really read it later. I think the way it progresses is brilliant. It works from the Drude model for metals to the Sommerfeld model, highlighting their successes and failures. Only then does it introduce crystal structures, motivated by the goal of understanding the Bloch model. In contrast, Kittel and Marder begin with crystal structures.
I think the approach of Ashcroft and Mermin has incredible value because it shows how good science is done: looking at experimental data and then developing the simplest possible model to explain the data, and using data to eliminate competing models. This is a great example of the method of multiple alternative hypotheses.

Tuesday, March 22, 2011

It is surprising to me how little theoretical attention has been given to this important question. The development of new high magnetic field facilities (50 to 100 Tesla) means that there will be a new generation of experimental data available. A few basic questions are the following:

What is the magnetic field scale that is required to significantly modify the metallic state of a strongly correlated material?

What is the relative importance of coupling of the field to orbital and spin degrees of freedom?

Several interesting experiments that are relevant are:

In heavy fermion metals a large magnetic field can suppress the effective mass enhancement.

In an organic charge transfer salt a magnetic field can be used to drive the system from the metallic state into the Mott insulating state [see this PRL].

In cuprates when one measures quantum oscillations is the role of the magnetic field just to suppress the superconducting state or does it also change the character of the metallic state (e.g., pseudogap or marginal Fermi liquid)?

However, it is important to appreciate the magnetic field scales involved here. If U/t is large enough that the quasi-particle weight Z=0.1 then it requires a field h=g mu_B B/2t =0.2 to be driven into the Mott phase. Moreoever, for h<0.1 there is only a very small change in Z. But, how big are these fields in Tesla?

If the tight binding parameter t ~ 30 meV, as it is in some organic charge transfer salts then h =0.1 for a field of 50 Tesla. Note, that in many transition metal oxides t may be orders of magnitude larger. Hence, I feel there must be different physics going on in some of these materials that are sensitive to smaller fields.

Similar considerations and concerns apply to papers by Lai and Motrunich on the effect of a magnetic field on frustrated ladders with Bose liquid ground states that consider the coupling of a field to orbital and spin degrees of freedom. The phase diagrams are interesting but the magnetic field scales required are on the scale of at least hundreds of Tesla.

[An earlier post discusses some of the interesting photophysics associated with these molecules].

Here are just a few of the key ideas. First, the ground and low lying singlet (covalent) states are written in a Rumer basis set of valence bond states [these are not orthogonal]. See R1 and R2 below for C4H6 (butadiene)

There is only one parameter in the Hamiltonian, lambda, and this is extracted from DFT based calculations. The eigenstates and energies are shown on the right.

For larger molecules one needs to include a larger number of basis states (e.g., see below for the case of hexatriene).

Simple energy correlation (Walsh) diagrams can then be used to understand how these states interact to produce the low lying excited states.

This approach is computationally cheap and gives reliable results. Moreover, it gives a chemically intuitive and physically transparent explanation for several important features:

the relative ordering of the excited states

the hardening of the -C=C- stretch frequency in the 2Ag excited state (see an earlier post Finding the lost twin on similar physics in other molecules)

the opposite bond alternation in the ground and 2Ag states

the presence of conical intersections between the ground state and 2Ag potential energy surfaces that are important for non-radiative decay

Friday, March 18, 2011

I have written many posts about organometallic compounds, particularly those that are on interest in organic LEDs and photovoltaic cells. Almost all quantum chemical treatments are based on density functional theory (DFT). But given that both transition metals and the excited states of conjugated organic molecules are typically strongly correlated I wonder about how reliable this is. For a while I have been wondering about a valence bond theory description of these materials. A key effect that needs to be taken into account is that of "back-bonding" and the Dewar-Chatt-Duncanson model. Hence, I was quite delighted when yesterday I stumbled across a 2007 Inorganic Chemistry paper, Valence Bond Approach to Metal-Ligand Bonding in the Dewar-Chatt-Duncanson Model.

The VB wavefunctions they include

A few key findings are:
-the importance of including back-bonding
-a VB wavefunction including back-bonding captures a lot of the correlation energy calculated by the CCSD(T) method
[n.b. there is typo on p. 11394 at the beginning of the paragraph, entitled "Correlation energy". VB-II should be VB-I]
-the component 3 of the VB function [see Figure above] corresponding to Pd2-L2+ has small weight.
-one must use "breathing orbitals" to get good results, i.e. when there are two electrons on Pd or L one makes one of the electrons more diffuse than the other [see Figure above].

Thursday, March 17, 2011

I really like the "popular" book The Cambridge Guide to the Material World by Rodney Cotterill. It was out of print for a while but I was delighted to see that the published issued a new expanded edition in 2008. A scan of the chapter on Crystal structures and symmetry from the first edition here. I encourage my solid state physics students to read this as it has beautiful pictures and gives a nice non-mathematical introduction.

This week Jure Kokalj [currently a postdoc with me] gave a nice Quantum Sciences seminar at UQ where he discussed his Ph.D work with Peter Prelovsek about spinon deconfinement in frustrated quantum spin chains. [See this PRB]. They used a new numerical method to calculate finite temperature dynamical correlation functions for the Heisenberg spin chain with next-nearest neighbour exchange interactions J'. When J' is large enough a gap opens in the spin excitation spectrum and there is spontaneous breaking of the discrete lattice symmetry and long range dimer spin correlations. The low lying excitations are deconfined spinons (spin-1/2 domain walls).
The new feature they found was that at non-zero temperature a large peak appears in the dynamical spin susceptibility at zero frequency and wave vector pi. I think the physics is that the finite temperature populates low lying triplet states which couple significantly to degenerate singlet excitations via spin flip operators. This peak should be observable with inelastic neutron scattering.

A few questions arise:

Is spinon deconfinement necessary for the appearance of this peak?

How does this compare to the dimerised Heisenberg spin chain in which the spinons are confined into triplons? (i.e. how does it related to this nice PRL by Kai Schmidt and Gotz Uhrig)?

Wednesday, March 16, 2011

Some people may attack me for this post. However, I actually think you can over-prepare for lectures. I notice that if I spend too much time preparing I start to go over the material too fast and also start to focus too much on little subtleties that I found interesting.
In contrast, if I have to think through how to do a problem on the board in real time it slows me down to pace that is more appropriate for students who are encountering the problem for the first time.
I am also told students like to see lecturers sweat it out!

Tuesday, March 15, 2011

Organic chemists are continually looking for new molecules which have large non-linear optical response, particularly in the near-infrared, motivated for the need for such materials in telecommunication systems. Cyanine dyes (see above) are one candidate material which have attracted a lot of attention, particularly by Seth Marder and collaborators. A key feature is that the more delocalised the electrons in the ground and excited states the larger the non-linear response. This occurs when these quantum states are superpositions of two valence bond structures with distinctly different charge distributions. [For a more detailed discussion see this forthcoming J. Chem. Phys. paper by Seth Olsen and I].

A recent development has been the synthesis and characterisation of a family of porphyrin dimer carbocations (shown above), as described in this Angewandte Chemie paper. The large optical response is perhaps surprising because it involves triple bonds near the central carbon cation [these are used because they bond better to porphyrin rings "because they cannot twist out of conjugation"]. Chemical shifts in 13C nmr are used to monitor the charge distribution on the central carbon atoms in the ground state.

The authors claim that the electrons are delocalised over about 18 conjugated bonds. This estimate was based on comparing the dominant absorption frequency to the predictions of an old "particle in a box" model. I did not find this particularly convincing, because the energy of the first excited state is largely determined by the matrix element between the two relevant diabatic states. The family of Creutz-Taube ions show how this can be tuned without increasing the length scale of the charge delocalisation [see this Chemical Reviews].
I think a better measure of the amount of charge delocalisation would be the oscillator strength of the transition or (probably) bond lengths and vibrational frequencies in different parts of the molecule.

A quantum chemical study in JACS compared these "porphocyanine" dyes to a new class of cyanine dyes. They discuss how the triple bond structures are resonant with various valence bond structures with double bonds.

Monday, March 14, 2011

I have written posts previously about the dangers of perfectionism in research and teaching. Hence, there was a quote in a New York Times article about the nuclear accidents in Japan that got my attention.

Mr. Diaz suggested that the Japanese might have acted too slowly to prevent overheating, including procedures that might have required the venting of small amounts of steam and radiation, rather than risk a wholesale meltdown. Fear among Japanese regulators over public reaction to such small releases may have delayed plant operators from acting as quickly as they might have, he said — a problem arising in part from the country’s larger nuclear regulatory culture.

“They would rather wait and do things in a perfect manner instead of doing it as good as it needs to be now,” Mr. Diaz said. “And this search for perfection has often led to people sometimes hiding things or waiting too long to do things.”

The fact that the night sky is dark implies a finite universe, and expansion or a hierarichial structure (Olber's paradox).

Hu contrasted Two views of quantum gravity.

1. Bottom up view
Quantum gravity = quantisation of general relativity
This is the more traditional view and has been dominant.

2. Top down view
Gravity is emergent and general relativity should be viewed as the "hydrodynamics" of some underlying "microscopic" theory.
This means that one must deal with a micro-macro transition as well as a quantum-classical one. This view has become more popular in the last 5 years.

It should be pointed out that Bob Laughlin has also advocated such a perspective. His book, A Different Universe, has a chapter, The Fabric of Space-Time, which ends with the claim that if Einstein were alive today he would,

conclude that his beloved principle of relativity was not fundamental at all but emergent - a collective property of the matter constituting space-time that becomes increasingly exact at long length scales but fails at short ones. This is a different idea from his original one but something fully compatible with it logically, and even more exciting and potentially important. It would mean that the fabric of space-time was not simply the stage on which life played out but an organizational phenomenon, and that there might be something beyond.

Friday, March 11, 2011

Starting to teach/lecture is a daunting and often overwhelming task. Many a young faculty member has seen their research program grind to a halt as they embark on teaching their first course. Furthermore, it can be a very stressful rather than an enjoyable experience.
Here are a few things I wish someone had told me or if they did that I had listened and taken to heart!

Your first lectures don't have to be perfect! Limit how many hours you spend on preparation. You can always polish lectures the second and third time you give the course.

Your goal should be to just survive.

Don't under-estimate how little students will learn or how little they know! Most of the new insights and subtleties you are getting as you prepare the lectures will be lost on the students. Just because they had covered a subject in a pre-requisite course does not all mean that they actually know and understand that material.

Technology should be your friend not a slave master. Blackboard, TurnItin, course blogs, online quizes, computer simulations etc. can greatly reduce your workload. But beware of getting bogged down with technical problems with making these things work. Never write your own software. It just isn't worth the time.

The textbook is your friend (and the students). The more you follow it the easier it is for everyone. Again, don't be a perfectionist and take material from lots of different books (unless you are teaching an advanced level graduate course).

Don't pander to unrealistic expectations of a small number of students or fear student evaluations.

Don't use Powerpoint too much. It may be slick but students will quickly go to sleep. Derivations should be done on the board by hand.

Keep it simple.

At the beginning clearly state the goal of the lecture. At the end clearly state the main point.

Enjoy! It is a great joy and privilege kindling student interest and understanding. An added bonus is how much you will learn too!

Thursday, March 10, 2011

I have been trying to learn some of the basics of infra-red spectroscopy of organic compounds and found this site for an organic chemistry lab course at University of Missouri helpful. Why should a quantum many-body theorist care?
Well, it turns out that the frequency, intensity, and lineshape associated with particular chemical bonds are quite sensitive to the type of bonding involved and the local environment of the bond, including valence states, orbital hybridisation, charge distribution, and the presence of resonating valence bond structures.
Previously I posted about the vibrational frequencies of O-H stretches associated with hydrogen bonding. The Table below, taken from here illustrates and summarises some of these effects.

But maybe someone could recommend a good book or review article. I struggled to find one online...

Table 1. A summary of the principle infrared bands and their assignments.R is an aliphatic group.

Tuesday, March 8, 2011

The movie The Inside Job is an Academy Award winning documentary which considers the origins of the Global Financial Crisis (GFC). It particularly focuses on conflicts of interest, including of economists in universities who write academic papers and books, sympathetic to vested interests, but do not reveal in those publications that they have received large consulting fees from those interests.

Last year, the director of the movie, Charles Ferguson, wrote a compelling and challenging article in the Chronicle of Higher Education, Larry Summers and the Subversion of Economics, which documents these conflicts of interest, and how they represent a serious problem for the university and government.

But are these economists corrupt? Have they been peddling the economic ideology of deregulated financial markets knowing that it is a load of crap? I don't know, but my gut tells me that's going too far. I think rather that they are the victims and perpetrators of groupthink. Having entered the world of high finance they become desensitized and sympathetic to the culture and stop questioning the worldview of those who are paying their consulting fees. They lose certain of their critical faculties - and that is a real problem, because the ability to examine issues critically is central to their identity as academics. In the end a guy like Frederic Mishkin comes off in the movie not as corrupt or malevolent, but simply clueless. He's so deep in the tank he doesn't know how deep he is. In the end my contempt for these guys is rooted not in my sense that they're corrupt but that they've made themselves lousy economists.

As I have said before, human nature is such that once large amounts of money, power, prestige, and/or bureaucracy become involved, the quest for the real truth becomes difficult. This applies in any research.

There are great videos on Youtube that can be used for teaching and to liven up seminars. I found the method described here works fine. I only post this because I seem to recall last time I did it was more involved..

Monday, March 7, 2011

This morning I read a paper, Estimating the hydrogen bond energy, which is one of the most downloaded papers from the Journal of Physical Chemistry. It considers a relatively simple criteria (going back to Davidson in 1967) for estimating a bond energy in terms of the two-center shared electron number, sigma.

It also connects to the natural bond orbital approach of Weinhold where a hydrogen bond D-H...A is viewed as an interaction between the unoccupied anti-bonding orbital of the DH bond and the the occupied nonbonded natural orbital (e.g. lone pair) of the acceptor atom A.

The authors perform quantum chemistry [most DFT with B2LYP-D] calculations for hundreds of H bonds. They find correlations between sigma and the bond energy, the H...A length, the shift in the D-H stretch frequency.

There were a couple of things I found strange about the paper.

1. Many quantities are calculated with quantum chemistry at different levels of theory and compared. But, I could never find a case where a calculated quantity was actually compared to an experimental value.

2. It makes the following claim:

Intramolecular hydrogen bonds are very interesting, but they are not accessible directly from experiment. Hence, theoretical results are the only reference data.

Surely this is an overstatement. Consider for example, the work discussed in this earlier post I made.

Sunday, March 6, 2011

There is an Opinion piece by Bob Herbert in the New York Times, College: The Easy Way that is worth reading. He discusses a systematic study which found a large fraction of American college graduates did not seem any better educated than when they started college. The study is published in a book, Academically Adrift by Richard Arum and Josipa Roska, which raises important and fundamental questions about the responsibilities of both students, faculty, and administrators.

Friday, March 4, 2011

particularly interesting. This material has a qualitatively different band structure from many of the kappa-(BEDT-TTF)2X family of organic charge transfer salts. In terms of the relevant tight-binding model t' > t so that it is closer to the limit of weakly coupled chains rather than to the square lattice [for background see the PRL referenced below and/or this recent review, which will appear in Reports of Progress in Physics]. The figure below shows the band structure and the Fermi surface for the new kappa-BETS material.

The observed pressure-temperature phase diagram is below. The system is always at half-filling and so the insulating state is a Mott-Hubbard insulator.

What is the symmetry of the pairing in the superconducting state.

Based on calculations reported in a PRL by Ben Powell and I, the superconductivity will have A_1 symmetry with "accidental" nodes in the energy gap. In contrast, in other kappa organics (which have t' < 0.8t or so) we predict A_2 symmetry with nodes required by symmetry.

The picture below shows the phase of the superconducting order parameter over the Brillouin zone for parameter values in a comparable regime to the new kappa-BETS material. The solid line is the Fermi surface (and the diagonals correspond to the Y and Z axes shown above.

Thursday, March 3, 2011

Eric Bittner, who has been a good source of humour for this blog, sent me an abstract for a chemistry paper. Do you think it is funny?
I actually did not laugh but groaned because it is a bit too close to the truth...
Actually, the chemistry abstract which made me laugh was this one, which was completely serious.

The phase mismatch gamma which occurs in the semi-classical quantisation condition (for the wavefunction) is related to the Maslov index (number of caustics) in the classical periodic orbit.
Aside: I am still confused as to exactly what a caustic is and how to visualise it.

This phase can be observed in the quantum Hall effect and deHaas van Alphen effect. In graphene it is found to have a different value (gamma=0) from conventional metals (gamma=1/2). This is usually stated as being due to Berry phase effects. But there is more to the story...

The phase parameter gamma_L which occurs in the energy quantisation condition is NOT necessarily the same as gamma. This is only the topological part of the Berry phase.
For a system with a gap the total Berry phase depends on the magnitude of the gap, whereas gamma_L does not.

Wednesday, March 2, 2011

The concept of a transition state is one of the key concepts in understanding chemical reactivity. It is the maximum on a potential energy surface (PES), for which the reactants and products are local minima. But there is more to the story...

It discusses the notion of the reaction force, the derivative of the potential energy, and how its sign and magnitude can be used to classify different parts of a chemical reaction. The blue dashed lines below define different regions: activation -> transition -> relaxation.

It turns out that some reactions are dominated by activation (the weakening of bonds) rather than transition (the breaking of bonds). Hence, in seeking to speed up a specific reaction with a catalyst one should target that part of the reaction.

What is new in this paper? They connect the reaction force and this division of the reaction path with a diabatic state analysis: which divides a reaction into electronic factors (which dominate the transition state) and nuclear reorganisation.

We teach it to undergraduates [as I am doing today!] and claim that it captures many properties of elemental metals? Then we say it works badly for cuprates and other strongly correlated electron metals. But, just how good is it? Surely, this should be in textbooks. But, it actually took me a long time to find the graph below. It shows the frequency dependence of the real and imaginary part of the dielectric constant for gold. The solid lines are the Drude predictions with two free parameters, the dc conductivity and the quasi-particle scattering time. The experimental data covers the range 50 to 20,000 cm-1.

Tuesday, March 1, 2011

Today Tony Wright is giving the weekly Quantum Science Seminar on Topological Insulators. Some people consider this new state of matter one of the most important discoveries and achievements of condensed matter theory in the past decade [see this Nature News feature]. Basically they are metallic states which occur on the surfaces of insulators as a result of topological effects associated with the band structure of the solid.
A really helpful introduction, The birth of topological insulators, by Joel Moore appeared in Nature last year.
I think a more accurate and helpful name for this class of materials might be something like "topological surface metals" or "topological metals". What do others think?

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About Me

I have fun at work trying to use quantum many-body theory to understand electronic properties of complex materials.
I am married to the lovely Robin and have two adult children and a dog, Priya (in the photo). I also write an even more personal blog Soli Deo Gloria [thoughts on theology, science, and culture]

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Although I am employed by the University of Queensland and funded by the Australian Research Council all views expressed on this blog are solely my own. They do not reflect the views of any present or past employers, funding agencies, colleagues, organisations, family members, churches, insurance companies, or lawyers I currently have or in the past have had some affiliation with.

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